It sounds like you're improvising either way... So why bother going to the coop?

If usually use my trainer as a work stand, and if I need one for the frame itself, I just go out and clamp the bike on my hitch bike rack on my car.

I haven't taken off a headset, but the last time I was messing with transferring the crown race from one fork to another - I basically used a rubber mallet and a wood paint stick - the combination let me gently hammer it off. Putting on a crown race, you can use a piece of pvc tubing. Now, my gentle hammering still took longer than the 5 seconds it takes for the guy with the proper tools at the bike shop.

If you're taking the fork to the coop anyways to do the crown race removal, you might as well just go to do everything.